Macbook Pro won't sleep with External Monitor (even when I tell it to from the Apple Menu)

Yeah, pretty much what I have in the subject. I've searched far and wide for solutions. Ive disonected hardware, reset smc, etc. If the macbook is open, I can make the whole system go to sleep from the Apple Menu. If I close the lid, the external display mimics sleep mode for an instant, then comes on again in clamshell mode, and does that same thing if I go and try to put the computer to sleep from the Apple Menu.

Any ideas? Everyone else who's had this problem seems to at least be able to manually put the computer to sleep when in clamshell mode, but I can't. It always wakes back up. I have no extra drives attached. Apps are all closed. Spotlight is no indexing, etc.